The statement of (REF ) is the aforementioned superposition principle, which is a modified version of the superposition principle [1]} in metric measure spaces, and the ones used in [2]}, [3]}. It allows one to essentially jump back and forth between the Liouville equation and the mean-field dynamics, and in particular, provides us with the non-negativity of \(\mathcal {I}_{\infty }\)  and uniqueness of gradient-flow solutions.
